The purpose of this paper is twofold. The first part explores \(\phi \) -divergence for two well-known mixture models and introduces three new extensions: relative \(\phi \) -divergence, Jensen- \(\phi \) -divergence, and \(\phi \) -symmetric divergence, forming a general class that encompasses various base measures. In the second part, we focus on \(\phi \) -Fisher information, enhancing its theoretical properties and examining its relationship with the proposed \(\phi \) - \(\chi ^2\) divergence measure. Additionally, we introduce Bayes- \(\phi \) -Fisher information, applying it to the arithmetic mixture model under uniform and beta prior distributions, and highlight its connections with other information measures. Finally, we present applications of the \(\phi \) -divergence and \(\phi \) -symmetric divergence measures in mixed reliability system lifetimes, logistic regression models, and image quality assessment. Our results demonstrate that both \(\phi \) -divergence and \(\phi \) -symmetric divergence serve as effective criteria for measuring similarity between two probability models.
